Parentheses in advanced Order of Operations: Solving an exercise

According to the order of operations, we first solve the expression in parentheses:

$5\times1=5$

Now we multiply:

$8\times5=40$

To solve the expression $(18-10)^2+3^3$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

• Step 1: Parentheses
  First, solve the expression inside the parentheses: $18-10$.
  $18-10 = 8$

• Step 2: Exponents
  Next, apply the exponents to the numbers:
  $(8)^2$ and $3^3$.
  $8^2 = 64$
  $3^3 = 27$

• Step 3: Addition
  Finally, add the results of the exponentiations:
  $64 + 27$
  $64 + 27 = 91$

Thus, the final answer is $91$.

To solve the expression $3-(5^2:5)^2+7^2$, we should follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Here are the steps to solve the expression:

1. Evaluate the exponents

• Calculate $5^2$ which equals $25$.

• Calculate $7^2$ which equals $49$.

2. Evaluate expressions inside parentheses

• The expression inside the parentheses is $5^2:5$ which simplifies to $25:5 = 5$.

3. Evaluate the expression inside the parentheses raised to a power

• The simplified expression now is $(5)^2$, which is $25$.

4. Substitute back into the expression

• The original expression now becomes: $3 - 25 + 49$.

5. Perform the addition and subtraction from left to right

• First, calculate $3 - 25$ which equals $-22$.

• Then, $-22 + 49$ equals $27$.

Therefore, the final result of the expression $3-(5^2:5)^2+7^2$ is $27$.

Let's walk through the steps to solve the expression $(4^2:8):2+3^2$ using the correct order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

• First, resolve the expression inside the parentheses: $4^2:8$

  • The exponent comes first:

    $4^2 = 16$, so the expression now is $16:8$.

• Next, perform the division inside the parentheses: $16:8$ equals 2. So the expression within the parentheses simplifies to 2.

• Now, we replace the original expression with this simplified result:

  $2:2+3^2$

• We perform the division: $2:2 = 1$.

• Substitute back into the expression:

  $1+3^2$

• Next, calculate the exponent:

  $3^2 = 9$.

• Finally, add the results:

  $1 + 9 = 10$.

Thus, the solution to the expression $(4^2:8):2+3^2$ is 10.